**Author details**

116 Recent Advances in Crystallography

respectively [9, 11].

minimum density, whereas the intermediate density rests with the detected cubic structure and finally the maximum density will be closer to the hexagonal close packing than to the simple cubic structure. This is contrary for the Lipid A-diphosphate invariant to the particle number density, *n*, and T=constant, but at very low *I* of M to mM NaCl or nM Ca2+,

The influence of the Lipid A-diphosphate crystal-crystal-coexistence within the crystallization process has also to be considered. Since there is a noticeable variation in large and small m-sized crystals as a function of polydispersity in size and charge, the ratio may be important so that the expanded Lipid A-diphosphate crystal phase is metastabile and a function of , T and I. As a result the density of the Lipid A-diphosphate nuclei is increasing with (*n*), which is contrary of the classical nucleation theory (CNT) [60]. According to this theory the density of the crystal is the same as the bulk density, or the density decreases

length and depends on the curvatures inside and outside of the nuclei, due to capillary forces [74, 75], which takes also the surface tension and the chemical potential () into account. Thus the assumption of CNT is independent on is no longer valid. This result in a decrease of the nucleation rate with an increase in supersaturation is governed by the increase in rather by slowing down the kinetics. There is also strong evidence that the 2 d crystals of Lipid A-diphosphate do not melt in a first-order transition but may be in secondorder transition. This behavior follows the theory developed by Kosterlitz, Thouless, Halperin, Nelson, and Young (KTHNY), which predicts that a third phase, namely the hexatic phase with short-range translational order and quasi-long-range order exists

The successful production of Lipid A-phosphate crystals makes it extremely useful to study various Lipid A-diphosphate assemblies of e.g. four, three, and penta- or hexaacylated Lipid A-phosphate approximants including those of modified disaccharide or monosaccharide moieties. This still remains to be elucidated. It was possible to construct different Wigner-Seitz polyhedra that make up the overall volume of the Frank-Kasper type unit cells with complexes comprised of Lipid A-diphosphate, antagonistic and non-toxic Lipid Aphosphate analogues depending on volume fraction, ( = 2 ·c), the nature of the counterions and temperature. They form by spontaneous self-assembly and appear to obey the principles of thermodynamically reversible self-assembly but once self-assembled strongly resist disassembly. Base on these principles, Lipid A-phosphate assemblies can be designed which form large unit cells by containing more than hundreds of Lipid Aphosphates. The range of Lipid A-phosphate structures may also be increased further by employing various different ("non-identical subunits") and identical subunits of Lipid Aphosphate in analogy with block copolymers. The rational design of such assemblies and the nucleation and creation of polymorphic Lipid A-phosphates production of mesoscopic suitable cellular networks, and structure-function relationships will be impacted by a theoretical and practical understanding of the spherical assemblies, rod-like assemblies and

*g* , where Lc is the capillary

with increasing of the Young-Laplace pressure, c = /Lc =

between crystal and liquid [60-64].

**5. Conclusion** 

Henrich H. Paradies, Hendrik Reichelt and Chester A. Faunce *The University of Salford, Joule Physics Laboratory, Manchester, United Kingdom* 

Peter Quitschau *Fachhochschule Südwestfalen, University of Applied Sciences, Biotechnology & Physical Chemistry, Iserlohn, Germany* 

Kurt Zimmermann *The Symbio Herborn Group Inc., Institute for Microecology, Herborn, Germany* 
